Structured Data Type - Array

1
Structured Data Type - Array

• Data types examined so far are atomic
• int, long
• float, double
• char
• Called simple data types because vars hold a
  single value
• If limited to simple data types, many
  programming applications are tedious
• Solution use structured data types - types that
  represent more than one piece of data

2
Outline

• Structured Types
• A. Arrays
• 1. Syntax of declaration
• 2. Layout in memory
• 3. Referencing array element
• a. Subscript use (abuse)
• b. Array elements as variables
• 4. Array Initialization
• 5. Processing arrays
• a. using loop
• b. types of processing
• 6. Passing array/part of array
• a. element of array
• b. entire array
• 7. Multidimensional arrays
• a. declaration
• b. referencing
• c. processing
• d. initialization

3
Outline (cont)

• Structured Types
• A. Arrays (cont)
• 6. Passing array/part of array
• a. element of array
• b. entire array
• 7. Multidimensional arrays
• a. declaration
• b. referencing
• c. processing
• d. initialization
• Techniques
• A. Sorting
• 1. What is sorted?
• 2. Selection sort
• 3. Insertion sort
• B. Searching
• 1. (Un)successful searches
• 2. Sequential search
• a. Unsorted array

4
Outline (cont)

• Techniques
• A. Sorting
• 1. What is sorted?
• 2. Selection sort
• 3. Insertion sort
• B. Searching
• 1. (Un)successful searches
• 2. Sequential search
• a. Unsorted array
• b. Sorted array
• 3. Binary search (sorted array)

5
Sample Problem

• Problem track sales totals for 10 people
• Daily data
• Employee Sale
• ---------- ----
• 3 9.99
• 7 16.29
• 9 7.99
• 3 2.59
• .
• .
• .
• 7 49.00

6
Representing Sales Data

• FILE sdata
• int numE
• float amtS
• float S0, S1, S2, S3, S4, S5, S6, S7, S8, S9
  0.0 / One var for each employee /
• if ((sdata fopen(DailySales,r)) NULL)
• printf(Unable to open DailySales\n)
• exit(-1)

7
Updating Sales Data

• while (fscanf(sdata,df,numE,amtS) 2)
• switch (numE)
• case 0 S0 amtS break
• case 1 S1 amtS break
• case 2 S2 amtS break
• case 3 S3 amtS break
• case 4 S4 amtS break
• case 5 S5 amtS break
• case 6 S6 amtS break
• case 7 S7 amtS break
• case 8 S8 amtS break
• case 9 S9 amtS break
• / What if 100 employees? /

8
Data Structure

• A Data Structure is a grouping of data items in
  memory under one name
• When data items same type, can use Array
• Using an array, we can set aside a block of
  memory giving the block a name
• Sales vs. S0
• S1
• S9

9
Parts of an Array
10
Declaring a 1D Array

• Syntax Type NameIntegerLiteral
• Type can be any type we have used so far
• Name is a variable name used for the whole array
• Integer literal in between the square brackets
  () gives the size of the array (number of
  sub-parts)
• Size must be a constant value (no variable size)
• Parts of the array are numbered starting from 0
• 1-Dimensional (1D) because it has one index
• Example
• float Sales10
• / float array with 10 parts numbered 0 to 9 /

11
Array Indices

• The array indices are similar to the subscripts
  used in matrix notation
• Sales0 is C notation for Sales
• Sales1 is C notation for Sales
• Sales2 is C notation for Sales
• The index is used to refer to a part of array
• Note, C does not check your index (leading to
  index-out-of-range errors)

0
1
2
12
Accessing Array Elements

• Requires
• array name,
• subscript labeling individual element
• Syntax namesubscript
• Example
• Sales5 refers to the sales totals for employee
  5
• Sales5 can be treated like any float variable
• Sales5 123.45
• printf(Sales for employee 5 7.2f\n,Sales5)

13
Invalid Array Usage

• Example
• float Sales10
• Invalid array assignments
• Sales 17.50 / missing subscript /
• Sales-1 17.50 / subscript out of range /
• Sales10 17.50 / subscript out of range /
• Sales7.0 17.50 / subscript wrong type /
• Salesa 17.50 / subscript wrong type /
• Sales7 A / data is wrong type /
• Conversion will still occur
• Sales7 17 / 17 converted to float /

14
Array Initialization

• Arrays may be initialized, but we need to give a
  list of values
• Syntax
• Type NameSize
• value0, value1, value2, , valueSize-1
• value0 initializes Name0, value1 initializes
  Name1, etc.
• values must be of appropriate type (though
  automatic casting will occur)

15
Array Initialization

• Example
• int NumDays12 31, 28, 31, 30, 31, 30, 31,
  31, 30, 31, 30, 31 / Jan is 0, Feb is 1,
  etc. /
• int NumDays13 0, 31, 28, 31, 30, 31, 30,
  31, 31, 30, 31, 30, 31 / Jan is 1, Feb is 2,
  /
• Note
• if too few values provided, remaining array
  members not initialized
• if too many values provided, a syntax error or
  warning may occur (extra values ignored)

16
Sales Data as an Array

• Recall data
• Employee Sale
• ---------- ----
• 3 9.99
• 7 16.29
• 9 7.99
• 3 2.59
• .
• .
• .
• 7 49.00
• Idea declare Sales as array, update array items

17
Updating Sales Data

• while (fscanf(sdata,df,numE,amtS) 2)
• switch (numE)
• case 0 Sales0 amtS break
• case 1 Sales1 amtS break
• case 2 Sales2 amtS break
• / cases 3-8 /
• case 9 Sales9 amtS break
• Q Whats the big deal??
• A Can replace entire switch statement with
• SalesnumE amtS

18
Updating with Arrays

• while (fscanf(sdata,df,numE,amtS) 2)
• SalesnumE amtS
• When referencing array element can use any
  expression producing integer as subscript
• is an operator, evaluates subscript expression
  then the appropriate location from the array is
  found
• Note, when we have an integer expression, we may
  want to check subscript before using
• if ((numE gt 0) (numE lt 9))
• SalesnumE amtS
• else
• / Problem employee /

19
Using Array Elements

• Array elements can be used like any variable
• read into
• printf(Sales for employee 3 )
• scanf(f,(Sales3))
• printed
• printf(Sales for employee 3 7.2f\n,Sales3)
• used in other expressions
• Total Sales0 Sales1 Sales2

20
Arrays and Loops

• Problem initialize Sales with zeros
• Sales0 0.0
• Sales1 0.0
• Sales9 0.0
• Should be done with a loop
• for (I 0 I lt 10 I)
• SalesI 0.0

21
Processing All Elements of Array

• Process all elements of array A using for
• / Setup steps /
• for (I 0 I lt ArraySize I)
• process AI
• / Clean up steps /
• Notes
• I initialized to 0
• Terminate when I reaches ArraySize

22
Initialize with Data from File

• if ((istream fopen(TotalSales,r)) NULL)
  
• printf(Unable to open TotalSales\n)
• exit(-1)
• for (I 0 I lt 10 I)
• fscanf(istream,f, (SalesI))
• fclose(istream)

• File TotalSales
• 1276.17 (Emp 0s Sales)
• 917.50 (Emp 1s Sales)
• 2745.91 (Emp 9s Sales)

23
Array Programming Style

• Define constant for highest array subscript
• define MAXEMPS 10
• Use constant in array declaration
• float SalesMAXEMPS
• Use constant in loops
• for (I 0 I lt MAXEMPS I)
• fscanf(istream,f,(SalesI))
• If MAXEMPS changes, only need to change one
  location

24
Summing Elements in an Array

• Sales
• 117.00 Sales0
• 129.95 Sales1
• 276.22 Sales2
• 197.81 Sales9
• total 0.0
• for (I 0 I lt MAXEMPS I)
• total SalesI

• I Total
• 0.00
• 0 117.00 (Emp 0 sales)
• 1 246.95 (0 1 sales)
• 2 523.17 (0 1 2 s)
• 9 1943.89 (All emps)

25
Maximum Element of an Array

• Sales
• 117.00 Sales0
• 129.95 Sales1
• 276.22 Sales2
• 197.81 Sales9
• maxS Sales0
• for (I 1 I lt MAXEMPS I)
• if (SalesI gt maxS)
• maxS SalesI
• / Note I starts at 1 /

• I maxS
• 117.00
• 1 129.95 (Max of 0,1)
• 2 276.22 (Max of 0,1,2)
• 9 276.22 (Max of all)

26
Printing Elements of an Array

• Sales
• 117.00 Sales0
• 129.95 Sales1
• 276.22 Sales2
• 197.81 Sales9
• printf(Emp Num Sales\n)
• printf(------- -----\n)
• for (I 0 I lt MAXEMPS I)
• printf(4d13.2f\n, I, SalesI)

• Output
• Emp Num Sales
• ------- ------
• 0 117.00
• 1 129.95
• 2 276.22
• 9 197.81

27
Passing an Element of an Array

• Each element of array may be passed as parameter
  as if it were variable of base type of array
  (type array is made of)
• When passing array element as reference parameter
  put in front of array element reference ( has
  higher precedence)
• does not hurt to put parentheses around array
  reference though
• example (Sales3)

28
Passing Array Element Examples

• Passing by value
• void printEmp(int eNum, float eSales)
• printf(4d13.2f\n, eNum, eSales)
• in main
• printf(Emp Num Sales\n)
• printf(------- -----\n)
• for (I 0 I lt MAXEMPS I)
• printEmp(I,SalesI)

• Passing by reference
• void updateSales(float eSales, float newS)
• eSales eSales newS
• in main
• while (fscanf(sdata,df, numE,amtS) 2)
• updateSales(
• (SalesnumE), amtS)

29
Passing Whole Array

• When we pass an entire array we always pass the
  address of the array
• syntax of parameter in function header
• BaseType NameforArray
• note, no value between - compiler figures out
  size from argument in function call
• in function call we simply give the name of the
  array to be passed
• since address of array is passed, changes to
  elements in the array affect the array passed as
  argument (no copy of array is made)

30
Passing Whole Array Example

• float calcSalesTotal(float S)
• int I
• float total 0.0
• for (I 0 I lt MAXEMPS I)
• total SI
• return total
• in main
• printf(Total sales is 7.2f\n,
• calcSalesTotal(Sales))

31
Size of an Array

• Sometimes we know we need an array, but not how
  big the array is going to be
• One solution
• allocate a very large array
• integer to indicate num elements of array in use
• loops use num elements when processing
• Example
• float SalesMAXEMPS
• int NumEmps 0
• processing
• for (I 0 I lt NumEmps I)
• process SalesI

32
Sorting Arrays

• One common task is to sort data
• Examples
• Phone books (by name)
• Checking account statement (by check )
• Dictionaries (by word)
• NBA scoring leaders (by points)
• NBA team defense (by points)

33
Sorting Order

• Team defense
• 90.0 Bulls
• 90.3 Heat
• 91.0 Knicks
• 98.9 76ers
• Sorted in ascending order

• Individual Scoring
• 31.0 Jordan
• 28.7 Malone
• 27.9 ONeill
• 0.3 Bricklayer
• Sorted in descending order

34
Sorting in Arrays

• Data sorted usually same type, sorted in array
• A A
• 6 1
• 4 4
• 8 6
• 10 8
• 1 10
• before after
• sort sort

35
Selection Sorting

• One approach (N is elements in array)
• 1. Find smallest value in A and swap with A0
• 2. Find smallest value in A1 .. AN-1 and swap
  with A1
• 3. Find smallest value in A2 .. AN-1 and swap
  with A2
• 4. Continue through AN-2

36
Selection Sort Example

• A A
• 6 1
• 4 Find smallest 4
• 8 and swap 8
• 10 with A0 10
• 1 6
• A A
• 1 1
• 4 Find 2nd 4
• 8 smallest and 8
• 10 swap with A1 10
• 6 6

• A A
• 1 1
• 4 Find 3rd 4
• 8 smallest and 6
• 10 swap with A2 10
• 6 8
• A A
• 1 1
• 4 Find 4th 4
• 6 smallest and 6
• 10 swap with A3 8
• 8 10

37
Selection Sort Notes

• If array has N elements, process of finding
  smallest repeated N-1 times (outer loop)
• Each iteration requires search for smallest value
  (inner loop)
• After inner loop, two array members must be
  swapped
• Can search for largest member to get
  descending-order sort

38
Selection Sort Algorithm

• For J is 0 to N-2
• Find smallest value in AJ, AJ1 .. AN-1
• Store subscript of smallest in Index
• Swap AJ and AIndex
• Find smallest in AJ..N-1
• Suppose J is 0
• Smallest A0
• for (K 1 K lt N K)
• if (AK lt Smallest)
• Smallest AK

• A K Smallest
• 6 6
• 4 1 4
• 8 2
• 10 3
• 1 4 1
• But we need location of smallest, not its value
  to swap

39
Selection Sort Algorithm

• Find location of smallest rather than value
• SmallAt 0
• for (K 1 K lt N K)
• if (AK lt ASmallAt)
• SmallAt K
• Swapping two elements
• Temp AJ
• AJ ASmallAt
• ASmallAt Temp

• J is 0, find smallest
• A K SmallAt
• 6 0
• 4 1 1
• 8 2
• 10 3
• 1 4 4
• Swap ASmallAt,A0

40
Code for Selection Sort

• for (J 0 J lt N-1 J) / 1 /
• SmallAt J / 2 /
• for (K J1 K lt N K) / 3 /
• if (AK lt ASmallAt) / 4 /
• SmallAt K / 5 /
• Temp AJ / 6 /
• AJ ASmallAt / 7 /
• ASmallAt Temp / 8 /

41
Selection Sort Example

• S J K Sml Effect
• 1 0 Start outer
• 2 0 Init SmallAt
• 3 1 Start inner
• 4 True, do 5
• 5 1 Update SmallAt
• 3 2 Repeat inner
• 4 False, skip 5
• 3 3 Repeat inner
• 4 False, skip 5
• 3 4 Repeat inner
• 4 True, do 5
• 5 4 Update SmallAt
• 6-8 Swap A0,A4
• 1 1 Repeat outer
• 2 1 Init SmallAt
• 3 2 Start inner
• 4 False, skip 5
• 3 3 Repeat inner

• S J K Sml Effect
• 4 False, skip 5
• 3 4 Repeat inner
• 4 False, skip 5
• 6-8 Swap A1,A1
• 1 2 Repeat outer
• 2 2 Init SmallAt
• 3 3 Start inner
• 4 False, skip 5
• 3 4 Repeat inner
• 4 True, do 5
• 5 4 Update SmallAt
• 6-8 Swap A2,A4
• 1 3 Repeat outer
• 2 3 Init SmallAt
• 3 4 Start inner
• 4 True, do 5
• 5 4 Update SmallAt
• 6-8 Swap A3,A4

42
Modularizing Sort

• Want to make sort more readable
• Also, make sort a separate function
• First make Swap a separate function
• Have to pass array elements as reference params

• void Swap(int n1, int n2)
• int temp
• temp n1
• n1 n2
• n2 temp
• for (J 0 J lt N-1 J)
• SmallAt J
• for (K J1 K lt N K)
• if (AK lt ASmallAt)
• SmallAt K
• Swap((AJ),(ASmallAt))

43
Modularizing Sort - Find Smallest

• Can make process of finding smallest a separate
  function
• Sort becomes
• for (J 0 J lt N-1 J)
• SmallAt
• findSmallest(A,J,N)
• Swap((AJ),
• (ASmallAt))
• Note whole array passed

• int findSmallest(
• int Aname, int J, int N)
• int MinI J
• int K
• for (K J1 K lt N K)
• if (AnameK lt
• AnameMinI)
• MinI K
• return MinI

44
Modularizing Sort Itself

• Can then make the sort routine itself a function
• Localize variables such as J, SmallAt in function
• Pass N only if different from size of array

• void sort(int A, int N)
• int J
• int SmallAt
• for (J 0 J lt N-1 J)
• SmallAt
• findSmallest(A,J,N)
• Swap((AJ),
• (ASmallAt))

45
Another Sort Insertion

• Idea sort like a hand of cards
• Algorithm
• Assume A0 .. A0 is sorted segment
• Insert A1 into sorted segment A0 .. 0
• Insert A2 into sorted segment A0 .. 1
• Insert A3 into sorted segment A0 .. 2
• continue until AN-1 inserted

46
Inserting into Sorted Segment
47
Insertion Sort Code

• void insertIntoSegment(int Aname, int J)
• int K
• int temp AnameJ
• for (K J (K gt 0) (AnameK-1 gt temp)
  K--)
• AnameK AnameK-1
• AnameK temp
• void sort(int A, int N)
• int J
• for (J 1 J lt N J)
• insertIntoSegment(A,J)

48
Searching Arrays

• Prob Search array A (size N) for value Num
• Example
• search array for a particular student score
• A N
• 6 5
• 4
• 8 Num
• 10 8
• 1
• Sequential search start at beginning of array,
  examine each element in turn until desired value
  found

49
Sequential Search

• Uses
• event-controlled loop
• must not search past end of array
• Code
• index 0 / 1 /
• while ((index lt N) (Aindex ! Num)) / 2 /
• index / 3 /
• When loop finishes either
• index is location of value or
• index is N
• Test
• if (index lt N) / 4 /
• printf(Found at d\n,index) / 5 /
• else
• printf(Not found\n) / 6 /

50
Sequential Search Example

• A N
• 6 5
• 4
• 8 Num
• 10 8
• 1

• S Num N index effect
• 8 5
• 1 0 init index
• 2 true, do 3
• 3 1 inc index
• 2 true, do 3
• 3 2 inc index
• 2 false, exit
• 4 true, do 5
• 5 print

51
Sequential Search Example

• S Num N index effect
• 5 5
• 1 0 init index
• 2 true, do 3
• 3 1 inc index
• 2 true, do 3
• 3 2 inc index
• 2 true, do 3
• 3 3 inc index
• 2 true, do 3
• 3 4 inc index
• 2 true, do 3
• 3 5 inc index
• 2 false, exit
• 4 false, do 6
• 6 print

• A N
• 6 5
• 4
• 8 Num
• 10 5
• 1

52
Sequential Search (Sorted)

• index 0 / 1 /
• while ((index lt N) (Aindex lt Num)) / 2 /
• index / 3 /
• if ((index lt N) (Aindex Num)) / 4 /
• printf(Found at d\n,index) / 5 /
• else
• printf(Not found\n) / 6 /
• Can stop either when value found or a value
  larger than the value being searched for is found
• While loop may stop before index reaches N even
  when not found (need to check)

53
Sorted Sequential Search Example

• A N
• 1 5
• 4
• 6 Num
• 8 5
• 10

• S Num N index effect
• 5 5
• 1 0 init index
• 2 true, do 3
• 3 1 inc index
• 2 true, do 3
• 3 2 inc index
• 2 false, exit
• 4 false, do 6
• 6 print
• Can do better when sorted

54
Binary Search

• Example when looking up name in phone book,
  dont search start to end
• Another approach
• Open book in middle
• Determine if name in left or right half
• Open that half to its middle
• Determine if name in left or right of that half
• Continue process until name is found (or not)

55
Code for Binary Search

• first 0
• last N - 1
• mid (first last) / 2
• while ((Amid ! num) (first lt last))
• if (Amid gt num)
• last mid - 1
• else
• first mid 1
• mid (first last) / 2

56
Binary Search Example

• 0 4 0 first Num 101
• 1 7
• 2 19
• 3 25
• 4 36
• 5 37
• 6 50 6 mid
• 7 100 7 first 7 first
• 8 101 8 mid -- found
• 9 205 9 last
• 10 220 10 mid
• 11 271
• 12 306
• 13 321 13 last 13 last

57
Binary Search Example

• 0 4 0 first Num 53
• 1 7
• 2 19
• 3 25
• 4 36
• 5 37
• 6 50 6 mid 6
  last
• 7 100 7 first 7 first 7 first, 7
  first
• 8 101 8 mid last,
• 9 205 9 last mid
• 10 220 10 mid
• 11 271
• 12 306
• 13 321 13 last 13 last

58
2-Dimensional Array Declaration

• Syntax BaseType NameIntLit1IntLit2
• Examples
• int Scores10010 / 100 x 10 set of scores /
• char Maze55 / 5 x 5 matrix of chars
  for Maze /
• float FloatM34 / 3 x 4 matrix of floats /

59
2D Array Element Reference

• Syntax NameintExpr1intExpr2
• Expressions are used for the two dimensions in
  that order
• Values used as subscripts must be legal for each
  dimension
• Each location referenced can be treated as
  variable of that type
• Example Maze32 is a character

60
2D Array Initialization

• 2D arrays can also be initialized
• Syntax
• BaseType NameDim1Dim2 val0, val1, val2,
  val3, val4,
• values are used to initialize first row of
  matrix, second row, etc.
• BaseType NameDim1Dim2
• val0-0, val0-1, val0-2, / first row /
• val1-0, val1-1, val1-2, / second row /

61
Processing 2D Arrays

• Use nested loops to process 2D array
• Type NameDim1Dim2
• for (J 0 J lt Dim1 J)
• for (K 0 K lt Dim2 K)
• process NameJK
• Example print 5x5 Maze
• for (J 0 J lt 5 J)
• for (K 0 K lt 5 K)
• printf(c,MazeJK
• printf(\n)

62
2D Example

• int Scores10010 / 10 scores - 100 students
  /
• int J
• int K
• for (J 0 J lt 100 J)
• printf(Enter 10 scores for student d ,J)
• for (K 0 K lt 10 K)
• scanf(d,(ScoresJK))

63
Passing 2D Array Parameters

• A single value can be passed as either a value or
  as a reference parameter
• 2D array may be passed by reference using name,
  syntax of parameter
• Type ParamNameDim2
• Dim2 must be the same literal constant used in
  declaring array
• Each row of 2D array may be passed as a 1D array

64
Passing Element of Array

• int Scores10010 / 10 scores - 100 students
  /
• int J
• int K
• void readScore(int score)
• scanf(d,score)
• for (J 0 J lt 100 J)
• printf(Enter 10 scores for student d ,J)
• for (K 0 K lt 10 K)
• readScore((ScoresJK))

65
Passing Row of Array

• int Scores10010 / 10 scores - 100 students
  /
• int J
• void readScore(int score)
• scanf(d,score)
• void readStudent(int Sscores, int Snum)
• int K
• printf(Enter 10 scores for student d
  ,Snum)
• for (K 0 K lt 10 K)
• readScore((SscoresK))
• for (J 0 J lt 100 J)
• readStudent(ScoresJ,J)

66
Passing Entire Array

• int Scores10010 / 10 scores - 100 students
  /
• void readScore(int score)
• scanf(d,score)
• void readStudent(int Sscores, int Snum)
• int K
• printf(Enter 10 scores for student d
  ,Snum)
• for (K 0 K lt 10 K)
• readScore((SscoresK))
• void readStudents(int Ascores10)
• int J
• for (J 0 J lt 100 J)
• readStudent(AscoresJ,J)

67
2D Array Example

• int Scores10010 / 10 scores - 100 students
  /
• int totalStudent(int Sscores)
• int J
• int total 0
• for (J 0 J lt 10 J)
• total SscoresJ
• return total
• float averageStudents(int Ascores10)
• int J
• int total 0
• for (J 0 J lt 100 J)
• total totalStudent(AscoresJ)
• return (float) total / 100

68
Multi-Dimensional Array Declaration

• Syntax
• BaseType NameIntLit1IntLit2IntLit3...
• One constant for each dimension
• Can have as many dimensions as desired
• Examples
• int Ppoints100256256 / 3D array /
• float TimeVolData100256256256
• / 4D array /

69
Multi-Dim Array Reference

• To refer to an element of multi-dimensional array
  use one expression for each dimension
• syntax
• NameExpr1Expr2Expr3 / 3D /
• NameExpr1Expr2Expr3Expr4 / 4D /
• etc.
• First expression - first dimension, 2nd
  expression - 2nd dimension, etc.
• C does not check dimensions